Electron energy relaxation time τ is one of the key physical parameters for electronic materials. In this study, we develop a new technique to measure τ in a semiconductor via monochrome picosecond (ps) terahertz (THz) pump and probe experiment. The special THz pulse structure of Chinese THz free-electron laser (CTFEL) is utilized to realize such a technique, which can be applied to the investigation into THz dynamics of electronic and optoelectronic materials and devices. We measure the THz dynamical electronic properties of high-mobility n-GaSb wafer at 1.2 THz, 1.6 THz, and 2.4 THz at room temperature and in free space. The obtained electron energy relaxation time for n-GaSb is in line with that measured via, e.g., four-wave mixing techniques. The major advantages of monochrome ps THz pump–probe in the study of electronic and optoelectronic materials are discussed in comparison with other ultrafast optoelectronic techniques. This work is relevant to the application of pulsed THz free-electron lasers and also to the development of advanced ultrafast measurement technique for the investigation of dynamical properties of electronic and optoelectronic materials.